1. To solve the system of equations −3x−4y=−23 and 3x−5y=5, we can use the method of elimination. Multiply the first equation by 3 and the second equation by -3 to eliminate the x term:
-3(-3x-4y) = -3(-23)
9x + 12y = 69
-3(3x-5y) = -3(5)
-9x + 15y = -15
Adding these two equations together, we eliminate the x term:
(9x + 12y) + (-9x + 15y) = 69 + (-15)
27y = 54
y = 2
Substitute this value of y back into either of the original equations, let's use the second equation:
3x - 5(2) = 5
3x - 10 = 5
3x = 15
x = 5
The solution to the system of equations is (5, 2).
Answer: C. (5, 2)
2. To determine the number of solutions of the system of equations 8x-6y=48 and 8x+6y=48, notice that both equations are equivalent when you multiply the second equation by -1:
8x-6y = 48
8x+(-6y) = 48
Since the equations are equivalent, they represent the same line. This means that the system of equations has an infinite number of solutions.
Answer: D. Infinite
3. To solve the system of equations 4x-6y=-48 and -2x+4y=30 using elimination with multiplication, first multiply the second equation by 2:
2(-2x+4y) = 2(30)
-4x + 8y = 60
Now add this equation to the first equation to eliminate the x term:
(4x - 6y) + (-4x + 8y) = -48 + 60
2y = 12
y = 6
Substitute this value of y back into either of the original equations, let's use the first equation:
4x - 6(6) = -48
4x - 36 = -48
4x = -12
x = -3
The solution to the system of equations is (-3, 6).
Answer: D. (-3, 6)
4. To solve the system of equations 3x-4y=40 and 5x-5y=55, we can use the method of elimination. Multiply the first equation by 5 and the second equation by 3 to eliminate the x term:
5(3x-4y) = 5(40)
15x - 20y = 200
3(5x-5y) = 3(55)
15x - 15y = 165
Subtracting these two equations, we eliminate the x term:
(15x - 20y) - (15x - 15y) = 200 - 165
-5y = 35
y = -7
Substitute this value of y back into either of the original equations, let's use the first equation:
3x - 4(-7) = 40
3x + 28 = 40
3x = 12
x = 4
The solution to the system of equations is (4, -7).
Answer: A. (4, -7)
5. To determine the number of solutions of the system of equations 12x-15y=18 and 4x-5y=6, notice that both equations are equivalent when you divide the first equation by 3 and divide the second equation by 2:
(1/3)(12x-15y) = (1/3)(18)
4x - 5y = 6
(1/2)(4x-5y) = (1/2)(6)
2x - (5/2)y = 3
The two resulting equations have the same slope but different y-intercepts. This means that the lines represented by the equations are parallel and will never intersect. Therefore, the system of equations has no solutions.
Answer: C. No solutions
1. Solve the system of two linear equations.−3x−4y=−23 3x−5y=5 (1 point)
A. (−5, 2) B. (−5,−2) C. (5, 2) D. (5,−2)
2. How many solutions does the system of equations have?8x−6y=48 8x+6y=48 (1 point)
A.None B. Two C. one D. Infinite
3. Solve the system of two equations using elimination with multiplication. 4x−6y=−48 −2x+4y=30 (1 point)
A.(3, 9) B.(−33,−9) C.(−21,−6) D.(−3, 6)
4. Solve the system of equations.3x−4y=40 5x−5y=55 (1 point)
A,(4,−7) B.(18, 7) C.(8,−3) D.(14, 3)
5. How many solutions does the system have?12x−15y=18 4x−5y=6 (1 point)
A. Two solutions B. one solution C. No solutions D. infinity Solutions
1 answer